The background description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the inventors hereof, to the extent the work is described in this background section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present disclosure.
In some systems, the performance achieved by error correcting codes may depend on the actual bit sequences or bit patterns of the codeword. For example, the error correcting performance for a first bit pattern, such as “010101,” may be statistically worse than the error correcting performance for a second bit pattern, such as “000000” or “111111.” In data storage systems, for instance, error correcting performance may decrease with the number of transitions (e.g., transitions from logical one to logical zero or vice versa) due to properties of the magnetic recording medium that make such transitions more prone to errors. In other words, in these systems, bit patterns with a large number of transitions may be more prone to errors than sequences with a smaller number of transitions.
In systems that exhibit such properties, error correction performance can be improved by constructing constraint codes and error correction codes (ECCs) that prevent bit patterns with a large number of transitions from occurring in the encoded data. For ease of exposition, we will sometimes refer to constraint codes and/or error correction codes as codes in the remainder of the descriptions. A specific example of constraint codes are Maximum Transition Run (MTR) codes, which are designed to completely eliminate specific transition patterns. While the avoidance of these specific patterns helps to improve the error correction performance, the use of such codes reduces the code rate, because the excluded patterns are no longer available for encoding. From an overall performance perspective, MTR codes may therefore suffer a performance loss in some scenarios.